Properties

Level 2
Symmetry odd
Weight 0
Character \( \chi_{2}(1,\cdot) \)
Multiplicity 1
Precision 3e-09
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1

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Spectral parameter

$R= 5.41733480684$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.380538572
4 0.500000000
5 -0.253812464
6 -0.269081407
7 0.397600583
8 0.353553390
9 -0.855190394
10 -0.179472514
11 1.201833974
12 -0.190269286
13 -0.948703217
14 0.281146052
15 0.0965854328
16 0.250000000
17 0.472807317
18 -0.604710927
19 -0.231256664
20 -0.126906232
21 -0.151302349
22 0.849824952
23 0.398077371
24 -0.134540702
25 -0.935579232
26 -0.670834478
27 0.705971504
28 0.198800279
29 0.830299583
30 0.0682962145
31 -0.985533801
32 0.176776695
33 -0.457344184
34 0.334325260
35 -0.100915977
36 -0.427595197
37 1.217345916
38 -0.163523155
39 0.361018168
40 -0.0897362573
41 -1.213893128
42 -0.106986917
43 -0.208503006
44 0.600916987
45 0.217057982
46 0.281483208
47 0.872905391
48 -0.0951346455
49 -0.841913787
50 -0.661554405
51 -0.179921421
52 -0.474351586
53 1.010367541
54 0.499197238
55 -0.305040442
56 0.140573026
57 0.0880020811
58 0.587110466
59 -0.823124818
60 0.0482927164
61 0.141375520
62 -0.696877633
63 -0.340024179
64 0.124999999
65 0.240792701
66 -0.323391174
67 1.611398664
68 0.236403658
69 -0.151483795
70 -0.0713583725
71 -0.662064805
72 -0.302355461
73 -1.524518974
74 0.860793551
75 0.356023986
76 -0.115628337
77 0.477849863
78 0.255278402
79 0.466176760
80 -0.0634531137
81 0.586540998
82 -0.858352069
83 -0.497617328
84 -0.0756511857
85 -0.120004402
86 -0.147433904
87 -0.315961044
88 0.424912530
89 0.315840081
90 0.153483287
91 -0.377205293
92 0.199038685
93 0.375033625
94 0.617237323
95 0.0586958235
96 -0.0672703505
97 -0.162357949
98 -0.595322953
99 -1.027796870
100 -0.467789617
101 0.128533754
102 -0.127223657
103 1.642947834
104 -0.335417237
105 0.0384024208
106 0.714437739
107 0.590326134
108 0.352985749
109 -1.193901507
110 -0.215696164
111 -0.463247077
112 0.0994001447
113 -0.759787797
114 0.0622268605
115 -0.101036976
116 0.415149783
117 0.811321836
118 -0.582037158
119 0.187988413
120 0.0341481080
121 0.444404954
122 0.0999674504
123 0.461933078
124 -0.492766846
125 0.491274135
126 -0.240433404
127 -1.144569597
128 0.0883883509
129 0.0793434340
130 0.170266149
131 -0.769099489
132 -0.228672096
133 -0.0919477813
134 1.139430923
135 -0.179184367
136 0.167162628
137 0.360856575
138 -0.107115212
139 1.540298168
140 -0.0504579813
141 -0.332174150
142 -0.468150504
143 -1.140183808
144 -0.213797589
145 -0.210740361
146 -1.077997706
147 0.320380762
148 0.608672945
149 0.123745404
150 0.251747119
151 1.198021429
152 -0.0817615345
153 -0.404340438
154 0.337890757
155 0.250140949
156 0.180508535
157 -0.908057784
158 0.329636898
159 -0.384483820
160 -0.0448681268
161 0.158275788
162 0.414747126
163 -1.012321539
164 -0.606946561
165 0.116079647
166 -0.351868604
167 1.134997795
168 -0.0534934548
169 -0.0999621908
170 -0.0848559257
171 0.197768481
172 -0.104251516
173 1.580219072
174 -0.223418161
175 -0.371986843
176 0.300458516
177 0.313230738
178 0.223332710
179 -1.944423784
180 0.108528949
181 -0.512271098
182 -0.266724129
183 -0.0537988600
184 0.140741586
185 -0.308977441
186 0.265188807
187 0.568235879
188 0.436452705
189 0.280694661
190 0.0415042095
191 0.565123516
192 -0.0475673252
193 0.785438782
194 -0.114804412
195 -0.0916308993
196 -0.420956903
197 -1.342195919
198 -0.726762121
199 0.884566070
200 -0.330777205
201 -0.613199344
202 0.0908871024
203 0.330127575
204 -0.0899607089
205 0.308101258
206 1.161739533
207 -0.340431983
208 -0.237175775
209 -0.277932192
210 0.0271546301
211 -0.0475778653
212 0.505183921
213 0.251941306
214 0.417423663
215 0.0529206648
216 0.249598615
217 -0.391848789
218 -0.844215850
219 0.580138266
220 -0.152520226
221 -0.448553806
222 -0.327565152
223 -1.539370469
224 0.0702865238
225 0.800098385
226 -0.537251111
227 0.912887960
228 0.0440010588
229 0.901960640
230 -0.0714439348
231 -0.181840342
232 0.293555228
233 0.793970702
234 0.573691237
235 -0.221554497
236 -0.411562472
237 -0.177398357
238 0.132927889
239 -0.861040125
240 0.0241463460
241 -1.050837222
242 0.314241728
243 -0.929172977
244 0.0706877382
245 0.213688202
246 0.326636061
247 0.219393957
248 -0.348438805
249 0.189362570
250 0.347383259
251 1.448663057
252 -0.170012080
253 0.478422923
254 -0.809332914
255 0.0456663775
256 0.0625000703
257 -0.260423008
258 0.0561042970
259 0.484017276
260 0.120396313
261 -0.710064085
262 -0.543835473
263 0.140625435
264 -0.161695359
265 -0.256444118
266 -0.0650168870
267 -0.120189346
268 0.805699331
269 -1.343029807
270 -0.126702483
271 0.980472013
272 0.118201821
273 0.143541014
274 0.255164124
275 -1.124410897
276 -0.0757418719
277 0.656524283
278 1.089155262
279 0.842819037
280 -0.0356792047
281 0.790860762
282 -0.234882624
283 -0.904475288
284 -0.331032385
285 -0.0223359831
286 -0.806231621
287 -0.482644581
288 -0.151177725
289 -0.776453277
290 -0.149015961
291 0.0617834054
292 -0.762259571
293 1.199923455
294 0.226543276
295 0.208919341
296 0.430396778
297 0.848460530
298 0.0875013493
299 -0.377657291
300 0.178012004
301 -0.0829009245
302 0.847129125
303 -0.0489120374
304 -0.0578141796
305 -0.0358828416
306 -0.285911775
307 -0.630769920
308 0.238924928
309 -0.625205032
310 0.176876255
311 -0.254590446
312 0.127639236
313 -0.530063178
314 -0.642093149
315 0.0863023663
316 0.233088376
317 0.194188015
318 -0.271871089
319 0.997882264
320 -0.0317266449
321 -0.224641725
322 0.111917869
323 -0.109339858
324 0.293270481
325 0.887586943
326 -0.715819469
327 0.454325574
328 -0.429176031
329 0.347067677
330 0.0820807188
331 0.972617769
332 -0.248808688
333 -1.041062540
334 0.802564635
335 -0.408993055
336 -0.0378255844
337 -1.023314314
338 -0.0706839639
339 0.289128601
340 -0.0600021756
341 -1.184447970
342 0.139843418
343 -0.732345961
344 -0.0737169291
345 0.0384484254
346 1.117383615
347 0.870240398
348 -0.157980472
349 0.845160774
350 -0.263034393
351 -0.669757494
352 0.212456207
353 1.718217144
354 0.221487572
355 0.168040132
356 0.157920034
357 -0.0715369232
358 -1.374915176
359 -0.270569171
360 0.0767417354
361 -0.946520223
362 -0.362230366
363 -0.169113200
364 -0.188602459
365 0.386941911
366 -0.0380415217
367 -1.151570606
368 0.0995193335
369 1.038109740
370 -0.218480135
371 0.401722715
372 0.187516800
373 0.736465032
374 0.401803468
375 -0.186948759
376 0.308618675
377 -0.787707897
378 0.198481094
379 -0.436187057
380 0.0293479030
381 0.435552932
382 0.399602629
383 0.211837240
384 -0.0336351950
385 -0.121284275
386 0.555389100
387 0.178309794
388 -0.0811790550
389 -1.727605303
390 -0.0647928713
391 0.188213876
392 -0.297661428
393 0.292671943
394 -0.949075819
395 -0.118321454
396 -0.513898383
397 0.749313173
398 0.625482884
399 0.0349896939
400 -0.233894758
401 -0.229089430
402 -0.433597415
403 0.934979087
404 0.0642668798
405 -0.148871417
406 0.233435459
407 1.463047675
408 -0.0636118443
409 -0.267529157
410 0.217860453
411 -0.137319844
412 0.821473909
413 -0.327274893
414 -0.240721725
415 0.126301487
416 -0.167708624
417 -0.586142841
418 -0.196527674
419 -1.543396781
420 0.0192012104
421 0.0572228903
422 -0.0336426211
423 -0.746500291
424 0.357218886
425 -0.442348696
426 0.178149336
427 0.0562109812
428 0.295163121
429 0.433883881
430 0.0374205232
431 1.529726664
432 0.176492889
433 0.637921335
434 -0.277078906
435 0.0801948712
436 -0.596950781
437 -0.0920581326
438 0.410219698
439 0.0192332952
440 -0.107848112
441 0.719996606
442 -0.317175412
443 -0.909020195
444 -0.231623554
445 -0.0801641785
446 -1.088499309
447 -0.0470899779
448 0.0497000689
449 1.402760162
450 0.565754983
451 -1.458898014
452 -0.379893895
453 -0.455893394
454 0.645509264
455 0.0957393172
456 0.0311134251
457 -0.771766744
458 0.637782501
459 0.333788486
460 -0.0505184814
461 0.593599149
462 -0.128580506
463 -0.846650650
464 0.207574867
465 -0.0951881872
466 0.561422080
467 0.637811352
468 0.405660930
469 0.640693002
470 -0.156662509
471 0.345550660
472 -0.291018542
473 -0.250586015
474 -0.125439499
475 0.216358921
476 0.0939942594
477 -0.864056628
478 -0.608847357
479 0.146063483
480 0.0170740209
481 -1.154900009
482 -0.743054111
483 -0.0602299271
484 0.222202355
485 0.0412084857
486 -0.657024545
487 0.968117426
488 0.0499838552
489 0.385227373
490 0.151100409
491 0.429223631
492 0.230966587
493 0.392571724
494 0.155134935
495 0.260867654
496 -0.246383467
497 -0.263237327
498 0.133899570
499 1.350535248